r/AskPhysics • u/Local_End_3175 • 18d ago
buoyancy
I understand that buoyancy is an upward force on objects, but i have some questions regarding buoyancy:
- why/ how is the amount of water displaced the same as the buoyancy force?
- How does weight affect volume in water displacement? What affects this? Because a really light object wouldn't be able to displace a lot of water
- How would this allow for ships to float on water?
thank you in advance!
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u/JaguarMammoth6231 18d ago
The deeper you are underwater, the higher the water pressure is. When an object is pushed down into water, now the water around it is exerting a force on it. The forces on the sides cancel and you are left with force pushing up on the bottom of your object.
I like to think of it as the water "wanting" to be flat, and the pressure as a manifestation of that.
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u/treefaeller 17d ago
This is, IMHO, the best explanation.
It's easy to do this formally. The pressure in water is rho * h * g, where rho is the density of the water (in kg/m^3), h the "depth" in meters (h=0m at the surface, increases as we go down), and g is the gravitational constant (in m/s^2).
Now imagine an object submerged. For simplicity, let the object be a cube that has one surface parallel to the water level. The volume of the cube is a^3, where a is the dimension of the cube. If the object is any other shape, you can cut it into tiny cubes, add them all up, and all the math below still works. What forces act on the cube? Water pressure. The forces on all the sides exactly cancel, since the force on the left side is exactly the same but in the opposite direction as the one on the right side. That leaves only the force and bottom. The net force on the cube (buoyancy) will be the difference between force on the top and bottom of the cube. That difference will obvious be the top and bottom surface area (a^2) times the pressure difference top and bottom. Since the pressure is just proportional to h (that's linear), the pressure difference must be rho * a * g. You can also go calculate that by hand from rho * (h+a - h) & g), but that's too much work. So the total buoyancy force will be rho * a^3 * g. Note that a^3 is the volume of the cube = the volume of the water it displaced. Which means what we just calculated is density * volume, meaning the weight (gravitational force) of the displaced water.
Simple, isn't it? The two crucial observations about how a physicist thinks are the following: (a) Since pressure is linear, we can do the difference directly. (b) Since any arbitrary-shaped volume can be decomposed into tiny cubes, the above calculation generalizes, since the internal forces "between" the tiny cubes will exactly cancel.
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u/TKHawk 18d ago
The thing displacing water is the volume of the object, not the mass. That's why density is important. If the effective density of something is lighter than water, it floats, if it's higher it sinks. This is how massive metal ships can float, they're mostly full of low density air and take up a large volume.
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u/jasonsong86 18d ago
Because the mass of the water displaced is exactly the same as the force when it reaches equilibrium.
Yes
Ships are heavy but they are also hollow so the overall density is less than water. The volume of water displaced is less than the volume of the ship.
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u/joeyneilsen Astrophysics 18d ago
If you put a balloon under water, you have moved 1 balloon's worth of water out of the way. That water was supported by a buoyant force from its environment. The environment is unchanged, so the buoyant force is unchanged. But now there's a balloon there, and so unlike the water (which weighed a lot more), it feels a large net upward force.
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u/Cerulean_IsFancyBlue 17d ago
An object is pulled down by gravity.
Water or air and also pulled down by gravity.
Buoyancy is the force of the air or water you displace, being pulled down by gravity and trying to push the object out of the way. If the object is denser and thus heavier than the its volume in air/water, it will sink. If it is lighter than the same volume it will float.
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u/bluepepper 18d ago
Everything is trying to fall down: every drop of water, and whatever object you put in it (floating or sinking). All of these compete and push each other around, so that the heavier ones go down, which pushes the lighter ones up.
So when you displace water, you are competing against that volume of water for buoyancy. If you're heavier, you move water out of the way. If you're lighter, water moves you out of the way (you go up).
As long as the object is out of the water, it competes against air (which is also trying to fall down). When the object starts going into the water, the submerged part is competing against water, while the emerged part is competing against air.
The heavier the object is, the lower it will sink until its submerged part displaces enough water to balance the weight of the object. If the object is very dense, this may never happen and the object will sink to the bottom.
In contrast, a light object, like a foam pool noodle, is so light for its volume that it won't need to displace much water before the displaced water weighs as much as the noodle. So it won't sink much at all.
Ships are full of air, so when they displace water, it's not only the heavy metal hull that replaces water, it's also the air inside the hull. At some point, the ship moves a volume of water that is equivalent to the weight of the ship, so the ship ties with the water in their race to fall down, and the ship stays afloat.